Illustrative Math Alignment: Grade 6 Unit 1

Topic

Equations

Description

Visual Model of an Equation. A visual model of an equation represents the numbers, operations, and equality using visuals. The example shows 1 + 2 = 3 with blocks illustrating the balance of the equation. This visual approach reinforces the foundational concept of equality and provides an intuitive way to understand equations, especially for visual learners.

Topic

Equations

Description

The Approximately Equal To Sign (≈) indicates that two expressions are close in value but not equal. Examples include estimating sums (58 + 49 ≈ 100), square roots (√50 ≈ 7), and function values (f(x) ≈ 25). This term relates to the topic by introducing estimation techniques, valuable for checking solutions or simplifying problems.

Topic

Equations

Description

Proportional To indicates a linear relationship between two variables. For example, distance (d) is proportional to time (t), written as d ∝ t. This term links linear equations to real-world relationships, reinforcing practical applications of mathematical concepts.

Topic

Equations

Description

Similar To. When two geometric shapes are similar, corresponding sides are proportional. ΔABC ~ ΔDEF; AB ∝ DE

The topic of this video is closely tied to Equations, providing an essential understanding of its fundamental concepts. This video explores the mathematics behind this topic by delving into how key principles are applied in practical contexts.

Topic

Equations

Description

Congruent To signifies that two geometric shapes are congruent, meaning their corresponding sides and angles are equal. For example, triangles ABC and DEF are congruent, so side AB equals side DE. This term introduces geometric equality, tying equations to geometric properties and congruence criteria.

Topic

Equations

Description

Assigning Values to Variables involves assigning a numerical value to a variable for evaluating functions. For instance, let x = 3 in f(x) = 2x + 8 yields f(3) = 14. This term supports understanding how to evaluate equations and functions by substituting values, a key step in problem-solving.

Topic

Equations

Description

A Conditional Equation is true only for specific variable values. Examples include x + 1 = 4 (x = 3), x2 - 25 = 0 (x = ±5), and 2x - 5 = x + 9 (x = 14). This term supports solving equations by emphasizing that solutions depend on satisfying the given conditions.

Topic

Equations

Description

A Constant Term in an algebraic equation is a number without a variable. Examples include 2 in x2 + 3x + 2 = 0, -10 in x3 - 2x2 + 4x - 10 = 0, and 5 in x4 - 2x3 + 4x2 - x + 5 = 0. This term explains the role of constants in equations, crucial for identifying and isolating terms when solving equations.

Topic

Equations

Description

The Division Property of Equality allows division by the same non-zero quantity on both sides of an equation, maintaining equality. For example, if a = b, then a / c = b / c, where c ≠ 0. Solving 5x = 15 yields x = 3 by dividing both sides by 5. This term builds on equality principles, showing another method to isolate variables and solve equations.

Topic

Equations

Description

Equality refers to a mathematical statement where two expressions are equal. Examples include 1 + 2 = 3 and x + 3 = 7, where both sides represent the same value. This term defines the core concept of equations, ensuring all manipulations preserve equality to find solutions.

This is the transcript for the video of same title. Video contents: In this episode of Algebra Applications, two real-world explorations of inequalities are developed: Hybrid Cars. An examination of the equations and inequalities that involve miles per gallon (mpg) for city and highway traffic reveals important information about hybrid cars and those with gasoline-powered engines. Floods in Venice. Venice experiences a great deal of flooding, and with the expected rise of sea levels over the next century, this ancient city is in peril. Through a series of inequalities, students analyze the impact of flooding.

This is the transcript for the video of same title. Video contents: With the increasing demand worldwide for cars, the cost of gasoline continues to rise. The need for fuel-efficient cars makes hybrids a current favorite. An examination of the equations and inequalities that involve miles per gallon (mpg) for city and highway traffic reveals important information about hybrid cars and those with gasoline-powered engines. Students use the Graphs and Geometry features of the TI-Nspire.

This is the transcript for the video of same title. Video contents: The city of Venice is slowly sinking into the Adriatic Sea. So what does a city whose streets are full of water do about flooding? Venice experiences a great deal of flooding, and with the expected rise of sea levels over the next century, this ancient city is in peril. Through a series of inequalities, students analyze the impact of flooding, rising sea levels, and sinking have on this grand, ancient city. Students use the Lists and Spreadsheets and the Program Editor features of the TI-Nspire.

This is the transcript for the video of same title. Video contents: In this episode of Algebra Applications, two real-world explorations are developed: Biology. Analyzing statistics from honey bee production allows for a mathematical analysis of the so-called Colony Collapse Disorder. Geology. Why do rivers meander instead of traveling in a straight line? In this segment the geological forces that account for a river??s motion are explained.

What Are Algebra Tiles?

What Are Algebra Tiles?

What Are Algebra Tiles?

Topic

Expressions and Equations

Description

This video explains solving one-step equations like x + 2 = 4 and x ÷ 2 = 4 with algebra tiles. It covers addition, subtraction, multiplication, and division operations. Key vocabulary includes one-step equations, zero pairs, and operations.

Topic

Expressions and Equations

Description

The video discusses solving two-step equations like 2x + 2 = 4 using algebra tiles. It shows a multi-stage process for isolating variables, including handling subtraction as addition. Key vocabulary includes two-step equations, multi-stage process, and integer tiles.

Topic

Expressions and Equations

Description

This video covers multi-step equations, such as 3x + 2 = x + 4, using algebra tiles. It demonstrates how to isolate variables through a multi-stage process involving addition and subtraction. Key vocabulary includes multi-step equations, isolation, and operations.

This is part of a collection of math worksheets on the topic of solving one-step equations.

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Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

Struggling with one step equations that don't include negative numbers? If so, this worksheet has you covered! With step-by-step instructions on the process, you'll be able to solve these equations in no time. Check it out!

This is part of a collection of math worksheets on the topic of solving one-step equations.

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of solving one-step equations.

Related Resources

Worksheet Library